I. By that which is self-caused, I mean that of which the essence
involves existence, or that of which the nature is only conceivable as
II. A thing is called finite after its kind, when it can be limited by
another thing of the same nature; for instance, a body is called
finite because we always conceive another greater body. So, also, a
thought is limited by another thought, but a body is not limited by
thought, nor a thought by body.
III. By substance, I mean that which is in itself, and is conceived
through itself: in other words, that of which a conception can be
formed independently of any other conception.
IV. By attribute, I mean that which the intellect perceives as
constituting the essence of substance.
I. Everything which exists, exists either in itself or in something
II. That which cannot be conceived through anything else must be
conceived through itself.
III. From a given definite cause an effect necessarily follows ; and,
on the other hand, if no definite cause be granted, it is impossible
that an effect can follow.
IV. The knowledge of an effect depends on and involves the knowledge
of a cause.
Prop. I. Substance is by nature prior to its
Proof.—This is clear from Deff. iii. and v.
Prop. II. Two substances, whose attributes are different, have nothing
Proof.—Also evident from Def. iii. For each must exist in itself, and
be conceived through itself ; in other words, the conception of one
does not imply the conception of the other.
Prop. III. Things which have nothing in common cannot be one the cause
of the other.
Proof.—If they have nothing in common, it follows that one cannot be
apprehended by means of the other (Ax. v.), and, therefore, one cannot
be the cause of the other (Ax. iv.). Q.E.D.
Prop. IV. Two or more distinct things are distinguished one from the
other, either by the difference of the attributes of the substances,
or by the difference of their modifications.
Proof.—Everything which exists, exists either in itself or in
something else (Ax. i.),—that is (by Deff. iii. and v.), nothing is
granted in addition to the understanding, except substance and its
modifications. Nothing is, therefore, given besides the understanding,
by which several things may be distinguished one from the other,
except the substances, or, in other words (see Ax. iv.), their
attributes and modifications. Q.E.D.
The book has the subtitle 'Ordine Geometrico demonstrata' (Proofs according to the method of geometry).
I am unsure what the result of formalization in Prolog will be, but I am curious.